%here we will plot several nonlinear functions using MATLAB vectors.

x = 0.01:.01:10; %vector of x values

%suppose we want to plot 1/x.

%Dividing a constant by a vector, multiplying vectors, or raising them to a
%power is not in general defined in mathematics.  So in MATLAB, if we typed
%y = 1/x, we would get an error.

%what we want to do is set each element of y to 1 divided by the
%corresponding element of x.  In MATLAB putting a period before an
%operation means "do this for each element of the vector individually."

y = 1./x; %so this works.

loglog(x,y,'k'); xlabel('x','FontSize',15); ylabel('y','FontSize',15);

%this works for more complicated functions.  Just put a period before each
% /, ^, or * symbol.
y = 1./sqrt(1+x.^2);